Question

Use Intermediate Value Theorem to prove that there exists some number c on [0,2] such that f(c)=0.
g(x)= 3^x-4/x

Answer 1

i would first evaluate at the endpoints g(0) and g(2), if they are 0 then you have your answer, if they arent 0 but one is < 0 and one is > 0 and g(x) is continuous then there exists a number c such that f(c) = 0

Answer 2

You can't put zero under the 4 though

Answer 3

i meant if g(x) is continuous on the interval [0,2]

Answer 4

I tried putting .01 instead of 0

Answer 5

oh, lol, my bad

Answer 6

forgot about divide by 0

Answer 7

Can you do .01 instead of 0?

Answer 8

since it is still a number b/w the interval?

Answer 9

is this for calc 1?

Answer 10

yes

Answer 11

have you learned local min an max?

Answer 12

not that i recall

Answer 13

ok you dont need to test the endpoints, if you can prove it within a smaller interval that is in the interval [0,2] then it is sufficient

Answer 14

so prove it for the interval [1,2]

Answer 15

and I think it should be f(x)= 3^x-4/x not g(x)= 3^x-4/x, right?